Tesla shares rose almost 9 percent before being halted pending news. The company had a market value of $58bn as of Monday's close.

But former SEC Chairman Harvey Pitt told CNBC he saw problems with Musk's tweets, noting that the mention of a go-private price is "highly unprecedented ... and raises significant questions about what his intent was". With approximately 170 million outstanding shares, Musk's proposed privatization of the company at $420 per share would require $71.4 billion, about a 17 percent increase.

Asked on Twitter whether Musk would continue to be CEO under such a scenario, he replied there would be "no change". Shares in Tesla were up sharply following the tweet, trading at $363 at the time of writing.

The announcement, made initially via Twitter, stunned investors and sent Tesla's stock price soaring as much as 13 percent. He would still allow employees to keep their shares unless they want to jettison theirs at Musk's $420 price, which he noted was 20 percent higher than the stock was as of the Q2 earnings call. He apologized for the comments last week in Tesla's latest conference call, saying "there's no excuse for bad manners".

Still, the tech-heavy NASDAQ exchange where Tesla is listed halted trading over the uncertainty of whether Musk's tweet may have violated any Securities and Exchange Commission rules that prevent company executives from making market-moving statements. "The 16 percent premium to the current share price may not be high enough to incentivize existing shareholders to support the sale".

Tesla has not confirmed whether the tweet was real - or if the CEO's account was hacked.

In 2013, he emailed SpaceX employees that he was "hesitant to foist being public" on the company "given the long term nature of our mission". I wanted to let you know my rationale for this, and why I think this is the best path forward.

When Musk responded to one Model 3 owner's praise for the electric auto on Twitter and mentioned the upcoming Autopilot upgrade, another person asked the CEO about the changes v9.0 would have on Model S and X vehicles.

"I can't believe this is something to bluff or make fun of", said George Galliers of Evercore ISI.